Temperature Activated Light with Relay?

I'd like to be able to read a temperature (ie. 150-200degC) and have it turn on a light when the temperature is reached. The temperature interface is a Type J Thermocouple wire. I've done some research today and I think I would need: Arduino, Relay, and Type J Thermocouple Amplifier. I would like to create something that is compact and not have wires and breadboards hanging around.

I was looking into Relay shields like the Seedstudio Relay Shield and then adding an appropriate thermocouple amplifier.

However, would it be easier to just get a R/C relay and connect that with a light and send PWM signals from an arduino?

http://www.dimensionengineering.com/datasheets/Battleswitch-diagram.jpg

This relay switch shows that it just activates from a PWM signal from RC receiver.

The "Battleswitch" is very expensive ($25) for what you're doing. By comparison a Seeedstudio Grove Relay is $2.90. Both require the same wiring but with the relay you'll just do a "digitalWrite(PIN, HIGH)" instead of using the Servo library attach/write/etc. with the Battleswitch.

Can the activated light be a LED? Because you won't need a relay to light one of those.